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The final word RE: tethered swimmer

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  • The final word RE: tethered swimmer

    Dear subscribers

    I must thank Peter Davidson for an excellent summary, regarding the
    technical aspects of the debate. I would also also like to add some
    thoughts about the why there is so much disagreement in the first
    place, and conclude my input with a final word.

    I think the some confusion arises from the introduction of the
    thermodynamic equation

    dE = dW + dQ

    which does not fall within the true definition (boundaries) of the
    biomechanic list.

    This equation is, however, the foundation of the industrial
    revolution, which permitted the energy trapped in inanimate
    fuel to be converted into "work" that could replace the
    manual labour of workmen. [This is the classical domain of the
    mechanical engineer]. In essence this is similar to the
    goal of biomechanists, who are often mechanical engineers looking
    for modern day applications of their trade. The goal of biomechanists
    is to try understand how men do things, so that we can do them

    However, (getting back to specifics) the thermo equation is merely a
    rather simple statement of transfer of energy.

    One of the key starting points in classical mechanics (the mechanics
    of the known (certain) universe, is that we can draw a "perfect
    boundary" around any system (including the know universe). In this
    case, there are two options available to us (and hence the two sides
    to the debate). First of all the boundary can be drawn either
    BEWTEEN the source and destination of the energy transfer, or
    alternatively it can always be drawn around both the source AND the
    destination of the energy transfer. [Another third option exists,
    which is to literally draw the line on considering the issue

    But in the case where the boundary includes both source and
    destination, the equation is rendered trivial (0=0). Therefore the
    statement that the work done during swimming is zero is often
    perceived as unhelpful. However, it does serve as an absolute check
    that your assumptions about the situations are correct. This is the
    real power of a zero balance. It is used with great effect by
    accountants when trying to balance a set of books. Accountants don't
    "make" money when they report a credit balance, they just ensure that
    the transfer is in their favour (a POSITIVE credit). However, the
    separate credit and debit balances must be equal. If they aren't, it
    is simply an indication that an error has occurred in the accounting
    procedure, and nothing else.

    What intrugues me was the equivalence or the terms on the right
    hand side of the equation (since the dW and dQ terms can be added).
    The fact is that dW is the "transfer of mechanical work", which can
    either be stored in an elevated weight, or immediately recovered by
    another adjacent system such as the water surrounding the swimmer. On
    the other hand, once dQ has been transferred to the lowest thermal
    reserviour it is "trapped". This is because at a molecular level the
    interactions are frictionless. Frictionless interactions cannot
    "grip" anything and hence cannot tranfer "mechanical" energy out of
    the system. Friction is in itself a boundary phenomenon -- which
    relates directly back choice of boundaries.

    We also need to know the ultimate destination of this heat flow
    (since we need to draw a boundary somewhere to moniter it).
    Also the isolation of the lowest thermal energy source i.e. the
    destination of all heat flow, eventually involves containment within
    a physical isothermal boundary. Any thermal momentum of the
    particles within this boundary must, on homgeneous average, be less
    than the surroundings. Therefore the internal energy within the
    boundary cannot 'pressure' our perfect boundary into displacing
    POSITIVELY in the direction of the force.

    [ work = force x displacement
    or work = pressure x area x displacement ]

    The interesting thing about the "perfect boundary" is that it is in
    essence an elimentary particle. (Here is where I get accused by
    just about everyone of digressing into theoretical physics - but why
    not?) Rhetorical answer (if there is such a thing): because it falls
    outside the "boundaries" of biomechanics and hence threatens our very

    Returning to theoretical physics, loosely intepreted by me,
    Heisenbergs uncertainty principle states that the product of the
    uncertainty in the position and velocity of an elimentary particle is
    a small, but IS a finite number, i.e. neither the velocity or the
    position of its boundary can be simultaneously determined (with
    perfect accuracy) at any given instant. As "proof" of this, I offer
    the interminable "tethered swimmer" debate!

    On one side the zero lobby argue that work is zero; but THIS answer
    cannot answer the question the non-zero lobby asks, i.e. what is the
    power of the swimmer? (Remember that power = work/time. If the
    work can be determined, then we can answer the ORIGINAL question
    by an exercise scientist about how exercise can affect performance.
    To those uninitiated by classical mechanics this might seem a
    reasonable question; by simply measuring the work at two discrete
    times before and after training, and subtracting them we can
    determine how effective the training was).

    To help out, the ever willing POSITIVE lobby contend that work IS
    being done, but are hard pressed to quantify this -- for example, it
    is one thing to say that the work is done at the skin of the swimmer,
    but it is completely another to try measure it! At this point,
    needing clarification, the subscriber referred the problem to BIOMCH-

    In reply, the POSITIVE lobby are in a sense correct, in that they are
    seeking to determine the credit balance (the non-zero work). BUT the
    zero-work lobby are trying to balance the books. It is important to
    realise that these objectives are complimentary AND simultaneous, or
    alternatively they they be held to be contradictory, and hence
    uncertain. It is a bit like trying to balance the Federal budget.

    It is at this stage helpful to try understand what are the intentions
    underlying these conflicting points of view? First of all, it can
    be held (rightly) that the quantity of the credit balance
    representing the positive work as measured by whatever means, is
    unreliable unless the energy books balance. But on the other hand,
    balancing the books without first determining the credit balance is a
    trivial task. I would contend that there are two equations and two
    variables, but that these equations are not independant. Therefore
    there is no currently known solution to the tethered swimmer problem.

    I would suggest (at the risk of persecution) that the bona fides of
    both lobbies in this debate need to be accepted. This would in fact
    reduce the "uncertainty" surrounding the debate to zero, and the
    debate will cease.

    (Never mind the fact that this "transfers" the "uncertainty" back to
    the person who asked the question in the first place .

    Some others might say, leave thermodynamics out of it, as there would
    then not be a problem...(or an answer).

    In conclusion, I would suggest that it is all about the choice of
    self-imposed boundaries -- not only the boundaries that define the
    swimmer, pool, weights and logically ultimately even the known
    universe; but also about the self-imposed boundaries of the engineer,
    scientist, accountant, physicist, biomechanist....

    One of the hallmarks of a genius is that it is suspected that he/she
    can live with contradiction. Also historically genii tend not to
    distinguish overduely between astronomy, art and science. Perhaps
    there is a morale in this for all of us non-genii in earthly
    (mechanical?) matters, but that is just my 2 cents worth.

    However for my reference for the day, I would like to mention a
    certain nameless parable. Authoritive ancient legend has it that
    everone was once working (no pun intended) to build a tower so
    high that they must eventually discover the ultimate TRUTH.

    The scribes say that it all broke down when everyone started to speak
    different languages, the "work"men, the slave drivers (the exercise
    scientists? the engineers, and accounts. Soon no one could
    understand anything anymore and the work had to stop due to the
    incessent quibbling. There seems to me to be a modern parallel here.

    If the truth be known, my final word in this debate is that the
    answer is (at least in principle) remains demonstrably "uncertain".


    Craig Nevin
    Biomedical Engineer
    Department of Physiology/Sports Science
    University of Cape Town, South Africa